An appeal brought by three former Labour MPs and a Tory peer facing trial over allegations that they fiddled their expenses was not an attempt to "take them above the law", three of the country's top judges heard today.

David Chaytor, Elliot Morley, Jim Devine and Lord Hanningfield are asking the Court of Appeal to overturn a ruling earlier this month that they are not protected from prosecution by parliamentary privilege.

Lord Chief Justice Lord Judge, sitting in London with Master of the Rolls Lord Neuberger and Sir Anthony May, heard that the four - who all deny theft by false accounting - did "not suggest that MPs are immune from the criminal law by reason of their status as MPs".

Nigel Pleming QC, for Chaytor, told the packed court: "This is not an attempt to take these defendants above the law.

"It is to ensure they, and indeed other members in a similar position, are adjudicated by the correct law and the correct body."

The central submission on their behalf was that any investigation into their expenses claims and the imposition of any sanctions "should lie within the hands of Parliament".

The decision under appeal was made by Mr Justice Saunders, sitting at Southwark Crown Court in central London, which resulted in the four having to face Crown Court trials.

He rejected argument that they were protected by parliamentary privilege and should be dealt with by Parliament alone.

It was said by the defendants that submitting an expenses form was part of the proceedings of Parliament, and therefore protected by parliamentary privilege.

Mr Pleming told the court today that the men submitted that "they have immunity from prosecution arising solely from the performance of their functions, or acts ancillary to the performance of those functions, as MPs when they were MPs".

Former Bury North MP Chaytor, 60, of Todmorden, Lancashire, is accused of falsely claiming rent on a London flat he owned, falsely filing invoices for IT work and renting a property from his mother, against regulations.

Ex-Scunthorpe MP Morley, 57, of Winterton, north Lincolnshire, is charged with falsely claiming £30,428 in interest payments between 2004 and 2007 towards a mortgage on his home which he had already paid off.

Devine, 57, of Bathgate, West Lothian, formerly MP for Livingston, is accused of wrongly submitting two invoices worth a total of £5,505 for services provided by Armstrong Printing. He faces a second charge alleging that he dishonestly claimed cleaning and maintenance costs of £3,240 by submitting false invoices from Tom O'Donnell Hygiene and Cleaning Services.

Former Essex County Council leader Lord Hanningfield, who is also known as Paul White, 69, of West Hanningfield, near Chelmsford, faces six charges of making dishonest claims for travelling allowances.

Each of the four defendants, who are all on unconditional bail, face separate criminal trials, pending the outcome of the appeal.

At the start of the proceedings, the appeal judges lifted statutory reporting restrictions which are normally applied to preparatory hearings in criminal matters.

Lord Judge said that the single issue in the appeal was "an issue of constitutional importance".

It was an issue which had to be addressed by the court, whether the appellants "had taken the point or not".

He said: "We are satisfied that the interests of justice require that both the argument as it develops before us and the judgment may be reported."

None of the appellants were present for the hearing.

Mr Pleming told the judges that the contention of the three former MPs was that the allegations against them "can only be determined by the House of Commons".

He said: "So there can be no doubt, and in the light of repeated media comment, the appellants emphasise that they do not contend at all that they are somehow 'above the law'.

"However, it is submitted that any investigation into their expenses claims and the imposition of any sanctions for abuse of the Additional Costs Allowance for MPs should lie within the hands of Parliament, ie for these appellants, with the House of Commons."

He added: "Nor do the appellants suggest that MPs are immune from the criminal law by reason of their status as MPs, even in relation to acts or omissions committed within the precincts of the Houses of Parliament.

"From many possible examples, it is not suggested that the Theft Act 1968 does not apply to an MP accused of theft of money or goods from others within the House, or that an MP cannot be tried for an assault even if committed within the House."

The House of Commons was itself a court of justice "with all the necessary powers to protect itself from abuse of its rules and procedures by those who are in contempt".

He told the judges that this was the first criminal prosecution "of members of the House of Commons in relation to conduct in Parliament, or based on members' dealings with Parliament, since the prosecution of Sir John Eliot and others in 1629.

In written argument before the court, Alun Jones QC, for Lord Hanningfield told the judges: "The substantive issue in this appeal is whether the matters under investigation in this trial are, as the appellant contends, 'proceedings in Parliament'.

"If they are the indictment must be quashed."

Lord Hanningfield's case was that available material "shows that the regulation of expenses and procedures for dealing with a failure to adhere to the rules are within the exclusive jurisdiction of the House of Lords".

Mr Jones said the true central issue at trial would be "Did Lord Hanningfield believe he was entitled to claim for the sums of money he did?"

The QC added: "If he did, by virtue of section 2(1) of the Theft Act 1968, he would have been acting honestly and thus entitled to an acquittal."

Lord Pannick QC, for the Crown, will argue during the appeal that Mr Justice Saunders correctly decided that parliamentary privilege did not prevent the prosecution of the defendants.

In his written case before the judges he asks them to dismiss the defendants' contentions that the hearing of the criminal charges would breach parliamentary privilege.

Mr Justice Saunders was "correct to conclude" that he could see "no logical, practical or moral justification for a claim for expenses being covered by privilege" and could see "no legal justification for it either".

The Crown say there are "strong reasons" why parliamentary privilege should be "confined to core parliamentary activities" - and argue that the submission of an expenses form was "not of itself the performance of the core functions of an MP or peer".

Lord Pannick states: "The Crown does not suggest that the defendants are making 'wild and extravagant' claims to privilege.

"But the Crown does respectfully suggest that it is one of the functions of this court to have regard, in defining the scope of privilege, to the need to ensure that privilege is confined in a reasonable and proportionate manner so as to avoid damaging the reputation of Parliament.